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Reference and Reference and Coterminal AnglesCoterminal Angles

By Henry BurkeBy Henry Burke

These are two or more angles in These are two or more angles in standard position with the same terminal standard position with the same terminal side. Standard position is where the side. Standard position is where the vertex is at the origin and the initial side vertex is at the origin and the initial side along the positive X-axis. These angles along the positive X-axis. These angles are found by taking the measure of the are found by taking the measure of the angle, and adding multiples of 360 angle, and adding multiples of 360 degrees. Every angle has infinite degrees. Every angle has infinite coterminal angles.coterminal angles.

What are coterminal What are coterminal angles?angles?

Coterminal angles Coterminal angles exampleexample

Image source: http://hotmath.com/hotmath_help/topics/coterminal-angles.html

This is the acute angle formed by the This is the acute angle formed by the terminal side of the given angle and the X-terminal side of the given angle and the X-axis. This is only if the angle is not one of axis. This is only if the angle is not one of the four quadrantal angles (90, 180, 270, the four quadrantal angles (90, 180, 270, 360). If the angle is greater than 360, or 360). If the angle is greater than 360, or less than 0, the reference angle can be less than 0, the reference angle can be found by using a coterminal angle.found by using a coterminal angle.

What is a reference What is a reference angle?angle?

Reference angle Reference angle exampleexampleImage source: http://img.sparknotes.com/figures/0/0954c20cdd40ed30b40d3e5107516db0/reference.gif

Quadrant 1= ActualQuadrant 1= Actual Quadrant 2= 180-angleQuadrant 2= 180-angle Quadrant 3= Angle-180Quadrant 3= Angle-180 Quadrant 4= 360-angleQuadrant 4= 360-angle

Reference Angle Reference Angle FormulasFormulas

Q: If the angle measure is 50 degrees in Q: If the angle measure is 50 degrees in standard position, find one coterminal standard position, find one coterminal angle.angle.

A: 50+360= 410 degreesA: 50+360= 410 degrees

Example 1Example 1

Q: If the angle measure is 110 degrees in Q: If the angle measure is 110 degrees in standard position, find the reference standard position, find the reference angle.angle.

A: 180-110= 70 degreesA: 180-110= 70 degrees

Example 2Example 2

Q: If the angle measure is -120 degrees, Q: If the angle measure is -120 degrees, find the reference and one coterminal find the reference and one coterminal angle.angle.

A: -120+360= 240 degrees (coterminal) A: -120+360= 240 degrees (coterminal) 240-180= 60 degrees (reference)240-180= 60 degrees (reference)

Example 3Example 3

Q: If the angle measure is 279 degrees, Q: If the angle measure is 279 degrees, find the reference and two coterminal find the reference and two coterminal angles.angles.

A: 360-279= 81 degrees (reference) A: 360-279= 81 degrees (reference) 279+360= 639 degrees (coterminal) 279+360= 639 degrees (coterminal) 279+(360(2))= 999 degrees (coterminal)279+(360(2))= 999 degrees (coterminal)

Example 4Example 4

If the angle measure is 336.7 degrees, If the angle measure is 336.7 degrees, find the reference and two coterminal find the reference and two coterminal angles!angles!

Final ProblemFinal Problem